%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO264+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 03:49:20 EDT 2022 % Result : Theorem 3.11s 1.34s % Output : Proof 4.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : GEO264+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n014.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 14:22:19 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.57 ____ _ % 0.49/0.57 ___ / __ \_____(_)___ ________ __________ % 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.57 % 0.49/0.57 A Theorem Prover for First-Order Logic % 0.49/0.57 (ePrincess v.1.0) % 0.49/0.57 % 0.49/0.57 (c) Philipp Rümmer, 2009-2015 % 0.49/0.57 (c) Peter Backeman, 2014-2015 % 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.57 Bug reports to peter@backeman.se % 0.49/0.57 % 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.57 % 0.49/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.73/0.96 Prover 0: Preprocessing ... % 2.62/1.23 Prover 0: Warning: ignoring some quantifiers % 2.76/1.26 Prover 0: Constructing countermodel ... % 3.11/1.34 Prover 0: proved (717ms) % 3.11/1.34 % 3.11/1.34 No countermodel exists, formula is valid % 3.11/1.34 % SZS status Theorem for theBenchmark % 3.11/1.34 % 3.11/1.34 Generating proof ... Warning: ignoring some quantifiers % 3.93/1.53 found it (size 4) % 3.93/1.53 % 3.93/1.53 % SZS output start Proof for theBenchmark % 3.93/1.53 Assumed formulas after preprocessing and simplification: % 3.93/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (line_connecting(v2, v0) = v6 & line_connecting(v1, v2) = v5 & line_connecting(v0, v1) = v4 & left_apart_point(v2, v4) & right_apart_point(v3, v6) & right_apart_point(v3, v5) & ~ left_apart_point(v3, v4) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (reverse_line(v10) = v12) | ~ (reverse_line(v9) = v11) | ~ distinct_lines(v9, v10) | ~ distinct_points(v7, v8) | left_apart_point(v8, v12) | left_apart_point(v8, v11) | left_apart_point(v8, v10) | left_apart_point(v8, v9) | left_apart_point(v7, v12) | left_apart_point(v7, v11) | left_apart_point(v7, v10) | left_apart_point(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v9) = v11) | ~ (reverse_line(v8) = v10) | ~ unequally_directed_lines(v7, v10) | ~ unequally_directed_lines(v7, v8) | unequally_directed_lines(v8, v11) | unequally_directed_lines(v7, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v9) = v11) | ~ (reverse_line(v8) = v10) | ~ unequally_directed_lines(v7, v10) | ~ unequally_directed_lines(v7, v8) | unequally_directed_lines(v8, v11) | unequally_directed_lines(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v9) = v11) | ~ (reverse_line(v8) = v10) | ~ unequally_directed_lines(v7, v10) | ~ unequally_directed_lines(v7, v8) | unequally_directed_lines(v8, v9) | unequally_directed_lines(v7, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (reverse_line(v9) = v11) | ~ (reverse_line(v8) = v10) | ~ unequally_directed_lines(v7, v10) | ~ unequally_directed_lines(v7, v8) | unequally_directed_lines(v8, v9) | unequally_directed_lines(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_through_point(v10, v9) = v8) | ~ (parallel_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection_point(v10, v9) = v8) | ~ (intersection_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (line_connecting(v10, v9) = v8) | ~ (line_connecting(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ incident_point_and_line(v9, v7) | ~ incident_point_and_line(v8, v7) | ~ distinct_points(v8, v9) | ~ equally_directed_lines(v7, v10) | before_on_line(v7, v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ before_on_line(v7, v8, v9) | incident_point_and_line(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ before_on_line(v7, v8, v9) | incident_point_and_line(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ before_on_line(v7, v8, v9) | distinct_points(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ before_on_line(v7, v8, v9) | equally_directed_lines(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v10) | ~ distinct_points(v7, v8) | ~ left_apart_point(v7, v9) | left_convergent_lines(v10, v9) | left_apart_point(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v9) = v10) | ~ left_apart_point(v7, v8) | ~ unequally_directed_lines(v8, v9) | distinct_lines(v8, v9) | left_apart_point(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ between_on_line(v7, v8, v9, v10) | before_on_line(v7, v10, v9) | before_on_line(v7, v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ between_on_line(v7, v8, v9, v10) | before_on_line(v7, v10, v9) | before_on_line(v7, v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ between_on_line(v7, v8, v9, v10) | before_on_line(v7, v9, v10) | before_on_line(v7, v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ between_on_line(v7, v8, v9, v10) | before_on_line(v7, v9, v8) | before_on_line(v7, v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ before_on_line(v7, v10, v9) | ~ before_on_line(v7, v9, v8) | between_on_line(v7, v8, v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ before_on_line(v7, v9, v10) | ~ before_on_line(v7, v8, v9) | between_on_line(v7, v8, v9, v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (reverse_line(v9) = v8) | ~ (reverse_line(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ~ apart_point_and_line(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | equally_directed_lines(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v7, v8) = v9) | ~ line(v7) | ~ point(v8) | line(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ line(v8) | ~ line(v7) | ~ unequally_directed_lines(v7, v8) | point(v9) | ? [v10] : (reverse_line(v8) = v10 & ~ unequally_directed_lines(v7, v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ apart_point_and_line(v9, v8) | ~ unequally_directed_lines(v7, v8) | ? [v10] : (reverse_line(v8) = v10 & ~ unequally_directed_lines(v7, v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ apart_point_and_line(v9, v7) | ~ unequally_directed_lines(v7, v8) | ? [v10] : (reverse_line(v8) = v10 & ~ unequally_directed_lines(v7, v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v8, v7) = v9) | ~ distinct_points(v7, v8) | ? [v10] : ? [v11] : (line_connecting(v7, v8) = v10 & reverse_line(v9) = v11 & equally_directed_lines(v10, v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ point(v8) | ~ point(v7) | ~ distinct_points(v7, v8) | line(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ distinct_points(v7, v8) | ~ apart_point_and_line(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ distinct_points(v7, v8) | ~ apart_point_and_line(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ distinct_points(v7, v8) | ? [v10] : ? [v11] : (line_connecting(v8, v7) = v10 & reverse_line(v10) = v11 & equally_directed_lines(v9, v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_convergent_lines(v7, v9) | right_convergent_lines(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_convergent_lines(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ right_convergent_lines(v7, v8) | left_convergent_lines(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_apart_point(v7, v9) | right_apart_point(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ left_apart_point(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ right_apart_point(v7, v8) | left_apart_point(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ unequally_directed_lines(v7, v9) | ~ unequally_directed_lines(v7, v8) | left_convergent_lines(v7, v9) | left_convergent_lines(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ unequally_directed_lines(v7, v9) | unequally_directed_opposite_lines(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | ~ unequally_directed_opposite_lines(v7, v8) | unequally_directed_lines(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ divides_points(v9, v7, v8) | left_apart_point(v8, v9) | left_apart_point(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ divides_points(v9, v7, v8) | left_apart_point(v8, v9) | right_apart_point(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ divides_points(v9, v7, v8) | left_apart_point(v7, v9) | right_apart_point(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ divides_points(v9, v7, v8) | right_apart_point(v8, v9) | right_apart_point(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ left_apart_point(v8, v9) | ~ right_apart_point(v7, v9) | divides_points(v9, v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ left_apart_point(v7, v9) | ~ right_apart_point(v8, v9) | divides_points(v9, v7, v8)) & ? [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v8) = v9) | unequally_directed_lines(v7, v9) | unequally_directed_lines(v7, v8)) & ? [v7] : ! [v8] : ! [v9] : ( ~ distinct_lines(v8, v9) | distinct_lines(v9, v7) | distinct_lines(v8, v7)) & ? [v7] : ! [v8] : ! [v9] : ( ~ distinct_points(v8, v9) | distinct_points(v9, v7) | distinct_points(v8, v7)) & ? [v7] : ! [v8] : ! [v9] : ( ~ left_convergent_lines(v8, v9) | left_convergent_lines(v8, v7) | unequally_directed_lines(v9, v7)) & ? [v7] : ! [v8] : ! [v9] : ( ~ left_apart_point(v8, v9) | distinct_points(v8, v7) | left_apart_point(v7, v9)) & ? [v7] : ! [v8] : ! [v9] : ( ~ unequally_directed_lines(v8, v9) | unequally_directed_lines(v9, v7) | unequally_directed_lines(v8, v7)) & ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ line(v7) | line(v8)) & ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ distinct_lines(v7, v8)) & ! [v7] : ! [v8] : ( ~ convergent_lines(v7, v8) | unequally_directed_lines(v7, v8)) & ! [v7] : ! [v8] : ( ~ convergent_lines(v7, v8) | unequally_directed_opposite_lines(v7, v8)) & ! [v7] : ! [v8] : ( ~ apart_point_and_line(v7, v8) | left_apart_point(v7, v8) | right_apart_point(v7, v8)) & ! [v7] : ! [v8] : ( ~ equally_directed_opposite_lines(v7, v8) | ~ unequally_directed_opposite_lines(v7, v8)) & ! [v7] : ! [v8] : ( ~ equally_directed_lines(v7, v8) | ~ unequally_directed_lines(v7, v8)) & ! [v7] : ! [v8] : ~ left_convergent_lines(v7, v8) & ! [v7] : ! [v8] : ( ~ left_apart_point(v7, v8) | apart_point_and_line(v7, v8)) & ! [v7] : ! [v8] : ~ left_apart_point(v7, v8) & ! [v7] : ! [v8] : ( ~ right_apart_point(v7, v8) | apart_point_and_line(v7, v8)) & ! [v7] : ! [v8] : ( ~ unequally_directed_lines(v7, v8) | ~ unequally_directed_opposite_lines(v7, v8) | convergent_lines(v7, v8)) & ! [v7] : ~ distinct_lines(v7, v7) & ! [v7] : ~ distinct_points(v7, v7) & ? [v7] : ? [v8] : (equally_directed_opposite_lines(v7, v8) | unequally_directed_opposite_lines(v7, v8)) & ? [v7] : ? [v8] : (equally_directed_lines(v7, v8) | unequally_directed_lines(v7, v8)) & ? [v7] : equally_directed_lines(v7, v7)) % 4.11/1.59 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields: % 4.11/1.59 | (1) line_connecting(all_0_4_4, all_0_6_6) = all_0_0_0 & line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1 & line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2 & left_apart_point(all_0_4_4, all_0_2_2) & right_apart_point(all_0_3_3, all_0_0_0) & right_apart_point(all_0_3_3, all_0_1_1) & ~ left_apart_point(all_0_3_3, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | left_apart_point(v1, v5) | left_apart_point(v1, v4) | left_apart_point(v1, v3) | left_apart_point(v1, v2) | left_apart_point(v0, v5) | left_apart_point(v0, v4) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ incident_point_and_line(v2, v0) | ~ incident_point_and_line(v1, v0) | ~ distinct_points(v1, v2) | ~ equally_directed_lines(v0, v3) | before_on_line(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ distinct_points(v0, v1) | ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v0, v1) | ~ unequally_directed_lines(v1, v2) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ unequally_directed_lines(v0, v1) | point(v2) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v1) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & equally_directed_lines(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & equally_directed_lines(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | right_apart_point(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_apart_point(v0, v1) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | left_convergent_lines(v0, v2) | left_convergent_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | unequally_directed_opposite_lines(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v0, v2) | ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1)) & ! [v0] : ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1)) & ! [v0] : ! [v1] : ( ~ equally_directed_lines(v0, v1) | ~ unequally_directed_lines(v0, v1)) & ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1) & ! [v0] : ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ~ left_apart_point(v0, v1) & ! [v0] : ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1)) & ! [v0] : ! [v1] : ( ~ unequally_directed_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1)) & ! [v0] : ~ distinct_lines(v0, v0) & ! [v0] : ~ distinct_points(v0, v0) & ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) & ? [v0] : ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1)) & ? [v0] : equally_directed_lines(v0, v0) % 4.11/1.61 | % 4.11/1.61 | Applying alpha-rule on (1) yields: % 4.11/1.61 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ distinct_points(v0, v1) | ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2)) % 4.11/1.61 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ incident_point_and_line(v2, v0) | ~ incident_point_and_line(v1, v0) | ~ distinct_points(v1, v2) | ~ equally_directed_lines(v0, v3) | before_on_line(v0, v1, v2)) % 4.11/1.61 | (4) ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) % 4.11/1.61 | (5) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) % 4.11/1.61 | (6) ! [v0] : ! [v1] : ~ left_convergent_lines(v0, v1) % 4.11/1.61 | (7) ! [v0] : ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1)) % 4.11/1.61 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v4)) % 4.11/1.62 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2)) % 4.11/1.62 | (10) line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2 % 4.11/1.62 | (11) right_apart_point(all_0_3_3, all_0_0_0) % 4.11/1.62 | (12) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ line(v0) | line(v1)) % 4.11/1.62 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1)) % 4.11/1.62 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ point(v1) | ~ point(v0) | ~ distinct_points(v0, v1) | line(v2)) % 4.11/1.62 | (15) ! [v0] : ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1)) % 4.11/1.62 | (16) ! [v0] : ~ distinct_lines(v0, v0) % 4.11/1.62 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0)) % 4.11/1.62 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ~ line(v0) | ~ point(v1) | line(v2)) % 4.11/1.62 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 4.11/1.62 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v2, v3) | ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3)) % 4.11/1.62 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) % 4.11/1.62 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 4.11/1.62 | (23) ? [v0] : equally_directed_lines(v0, v0) % 4.11/1.62 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2)) % 4.11/1.62 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1)) % 4.11/1.62 | (26) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ~ distinct_lines(v0, v1)) % 4.11/1.62 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v1, v2)) % 4.11/1.62 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) % 4.11/1.62 | (29) ! [v0] : ! [v1] : ( ~ unequally_directed_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1)) % 4.11/1.62 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2)) % 4.11/1.62 | (31) left_apart_point(all_0_4_4, all_0_2_2) % 4.11/1.62 | (32) ! [v0] : ! [v1] : ~ left_apart_point(v0, v1) % 4.11/1.62 | (33) ? [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) % 4.11/1.62 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v2)) % 4.11/1.62 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2)) % 4.11/1.62 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ before_on_line(v0, v3, v2) | ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3)) % 4.11/1.62 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v0, v2) | ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1)) % 4.11/1.62 | (38) ! [v0] : ~ distinct_points(v0, v0) % 4.11/1.62 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ line(v1) | ~ line(v0) | ~ unequally_directed_lines(v0, v1) | point(v2) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 4.11/1.62 | (40) ? [v0] : ! [v1] : ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) % 4.11/1.62 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2)) % 4.11/1.62 | (42) ! [v0] : ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) | ~ unequally_directed_opposite_lines(v0, v1)) % 4.11/1.62 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 4.11/1.62 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ~ apart_point_and_line(v0, v2)) % 4.11/1.63 | (45) right_apart_point(all_0_3_3, all_0_1_1) % 4.11/1.63 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ left_apart_point(v0, v1) | ~ unequally_directed_lines(v1, v2) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) % 4.11/1.63 | (47) line_connecting(all_0_4_4, all_0_6_6) = all_0_0_0 % 4.11/1.63 | (48) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) % 4.11/1.63 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4)) % 4.11/1.63 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1)) % 4.11/1.63 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & equally_directed_lines(v3, v4))) % 4.11/1.63 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3)) % 4.11/1.63 | (53) ? [v0] : ! [v1] : ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) % 4.11/1.63 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ distinct_points(v0, v1) | ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & equally_directed_lines(v2, v4))) % 4.11/1.63 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ apart_point_and_line(v0, v2)) % 4.11/1.63 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0)) % 4.11/1.63 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v0) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 4.11/1.63 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3)) % 4.11/1.63 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1)) % 4.11/1.63 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ right_apart_point(v0, v1) | left_apart_point(v0, v2)) % 4.11/1.63 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_apart_point(v0, v2) | right_apart_point(v0, v1)) % 4.11/1.63 | (62) ~ left_apart_point(all_0_3_3, all_0_2_2) % 4.11/1.63 | (63) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) % 4.11/1.63 | (64) line_connecting(all_0_5_5, all_0_4_4) = all_0_1_1 % 4.11/1.63 | (65) ? [v0] : ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1)) % 4.11/1.63 | (66) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) % 4.11/1.63 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ left_convergent_lines(v0, v2)) % 4.11/1.63 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 4.11/1.63 | (69) ? [v0] : ! [v1] : ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) % 4.11/1.63 | (70) ! [v0] : ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) % 4.11/1.63 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | ~ unequally_directed_lines(v0, v1) | left_convergent_lines(v0, v2) | left_convergent_lines(v0, v1)) % 4.11/1.63 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2)) % 4.11/1.63 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ unequally_directed_lines(v0, v2) | unequally_directed_opposite_lines(v0, v1)) % 4.11/1.63 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2)) % 4.11/1.63 | (75) ! [v0] : ! [v1] : ( ~ equally_directed_lines(v0, v1) | ~ unequally_directed_lines(v0, v1)) % 4.11/1.63 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ unequally_directed_lines(v0, v3) | ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2)) % 4.11/1.63 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ apart_point_and_line(v2, v1) | ~ unequally_directed_lines(v0, v1) | ? [v3] : (reverse_line(v1) = v3 & ~ unequally_directed_lines(v0, v3))) % 4.52/1.64 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2)) % 4.52/1.64 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | left_apart_point(v1, v5) | left_apart_point(v1, v4) | left_apart_point(v1, v3) | left_apart_point(v1, v2) | left_apart_point(v0, v5) | left_apart_point(v0, v4) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) % 4.52/1.64 | % 4.52/1.64 | Instantiating formula (32) with all_0_2_2, all_0_4_4 and discharging atoms left_apart_point(all_0_4_4, all_0_2_2), yields: % 4.52/1.64 | (80) $false % 4.52/1.64 | % 4.52/1.64 |-The branch is then unsatisfiable % 4.52/1.64 % SZS output end Proof for theBenchmark % 4.52/1.64 % 4.52/1.64 1055ms %------------------------------------------------------------------------------